To determine Roman's rate of speed for each training session and ascertain whether his speed increased or decreased, we need to calculate the rate for each session using the formula:
\[ \text{Rate} = \frac{\text{Distance}}{\text{Time}} \]
Session 1:
- Time: \( \frac{2}{125} \) hr
- Distance: \( \frac{9}{10} \) mile
\[ \text{Rate} = \frac{\frac{9}{10}}{\frac{2}{125}} = \frac{9}{10} \times \frac{125}{2} = \frac{9 \times 125}{10 \times 2} = \frac{1125}{20} = 56.25 \text{ miles per hour} \]
Session 2:
- Time: \( \frac{3}{200} \) hr
- Distance: \( \frac{11}{12} \) mile
\[ \text{Rate} = \frac{\frac{11}{12}}{\frac{3}{200}} = \frac{11}{12} \times \frac{200}{3} = \frac{11 \times 200}{12 \times 3} = \frac{2200}{36} \approx 61.11 \text{ miles per hour} \]
Session 3:
- Time: \( \frac{3}{250} \) hr
- Distance: \( \frac{17}{20} \) mile
\[ \text{Rate} = \frac{\frac{17}{20}}{\frac{3}{250}} = \frac{17}{20} \times \frac{250}{3} = \frac{17 \times 250}{20 \times 3} = \frac{4250}{60} \approx 70.83 \text{ miles per hour} \]
Summary of Rates:
- Session 1: approximately 56.25 miles per hour
- Session 2: approximately 61.11 miles per hour
- Session 3: approximately 70.83 miles per hour
Conclusion:
Roman's rate increased from session to session.
So, the answers are:
- Roman's rate increased.
- His unit rate for Session 1 was about 56.25 miles per hour (closest to 56.3).
- Session 2 was approximately 61.11 miles per hour (closest to 61.1).
- Session 3 was about 70.83 miles per hour (closest to 70.8).
3 answers